Now. now, lets not nit pick this to death. This is an idealised thought experiment, "forever" simply means "for a long time", like we have a stable situation where the Slinky keeps on hopping until we get bored watching it and go off and have a beer.

I think it's incorrect to compare the escalator to a staircase, the dynamics are different. Dave's bouncing ball is also dynamically different than a Slinky, but if you prefer, try it with the ball. I suspect that if the ball hops "down" forever, the Slinky will also.

Dave's bouncing ball is also dynamically different than a Slinky, but if you prefer, try it with the ball. I suspect that if the ball hops "down" forever, the Slinky will also.

I only used the ball because it is easier to visualize a simple ball descending over an arbitrarily long distance than a slinky, which might intuitively seem like it's going to run out of energy. No one has trouble envisioning why a ball could bounce all the way down a staircase of arbitrary height. It's jsut a short step to recognize that a slinky can do the same thing.

In practice, the ball or slinky might bounce this way or that and eventually stop, but ideally, it is using potential energy to keep going. There is no principle that says the ball or the slinky will come to a stop.

How? Ideally, an escalator is identical to an infinitely long stairway.

There is a very fundamental difference. On an infintely long stairway, the energy that keeps the slinky moving is coming from its weight (acting over the whole of the spring) as it descends. On the escalator, the energy is coming from the reaction from the ends of the spring and the steps (and ultimately from the motor driving the escalator upwards, of course).

After a few decades doing dynamics for a living, it's far from obvious to me whether they are equivalent or not, but I don't have enough free time to spend a couple of days (at least) thinking hard about the problem to form an opinion.

The bouncing ball is simpler to understand, because the escalator is basically the same as somebody hitting the ball with a bat at the same time as it hits the steps. There doesn't seem to be any problem about maintaining the height of the ball for an "infinite" number of bounces, but there DOES seem to be a problem stopping the ball moving horizontally in one direction and therefore descending the escalator whether or not it is moving upwards. I can't see how to counteract that without some "backspin" on the ball, and it's not clear to me how the spin could be maintained indefinitely.

There is a very fundamental difference. On an infintely long stairway, the energy that keeps the slinky moving is coming from its weight (acting over the whole of the spring) as it descends. On the escalator, the energy is coming from the reaction from the ends of the spring and the steps (and ultimately from the motor driving the escalator upwards, of course).

Sorry, not seeing it. Are you saying that the ball/slinky can "tell" the difference between a staircase and an escalator? If I constructed them and put you on one of them in a darkened room, what tests would you conduct to determine which one you're on? (Ignoring real-world limits such as altitude and gravitational gradient).

...there DOES seem to be a problem stopping the ball moving horizontally in one direction and therefore descending the escalator whether or not it is moving upwards. I can't see how to counteract that without some "backspin" on the ball, and it's not clear to me how the spin could be maintained indefinitely.

You've lost me. Why would you want to counteract horizontal movement? You want it to go over each step.

There is a very fundamental difference. On an infintely long stairway, the energy that keeps the slinky moving is coming from its weight (acting over the whole of the spring) as it descends. On the escalator, the energy is coming from the reaction from the ends of the spring and the steps (and ultimately from the motor driving the escalator upwards, of course).

Principle of relativity (paraphrased): You can't tell the difference between you moving in one direction and the rest of the world moving in the other direction.
The escalator can represent "the rest of the world" in this situation.

Hhhmmm, I am afraid I may be totally off, but I am going to stick my nose in here...

I think that a stairway and an escalator provide TOTALLY different experience...for one, an escalator has continuous input of energy; whereas the stairway is just there. As mentioned before, an escalator would slap from below a bouncing ball, whereas a stairway wouldn't.

Now a few questions.

What would happen if I drop a ball with no spin and no horizontal speed from a given height and down into the middle of a stairway? I presume that it would bounce a few times and eventually come to rest in the very same step it landed the first time.

What would happen if I do the same thing as above, but this time I drop the ball in the middle of an escalator? .... Well, I presume that if the escalator is moving a constant speed, the ball may initially gain a bit of height, maybe a lot, but I think it will eventually develop some back spin that would allow it to climb back down...then again, I am just speculating...

Any thoughts so far?

As far as the slinky goes...

I think the phenomena is different since the slinky is always in contact with the escalator and so, all of it is being translated....unlike the ball where the ball spends most of its time up in the air.

So, I think one can find a constant speed setting for an escalator as to make a slinky stay put in space.

...but that's just my opinion.

P.D. by the way, just to add that the reason I see for developing a back spin at the escalator is because the escalator step is moving at an angle but but the ball is coming down vertically...think about it, try to land on a moving surface while your center of gravity is coming down...you will feel that your feet are going away from under you...right?

If an ideally perfect Slinky will keep moving down a staircase at a constant speed (no matter how long the staircase might be), then it will keep moving in just the same way on an escalator adjusted to that speed.

Look at this from a point of view of Galilean Relativity. A staircase is at rest in the inertial frame defined by the Earth. You can also define an inertial frame in which the steps in the centre portion of the escalator are at rest. The force of gravity will be the same in both frames. For the Slinky, there is no difference.

There is a very fundamental difference. On an infintely long stairway, the energy that keeps the slinky moving is coming from its weight (acting over the whole of the spring) as it descends. On the escalator, the energy is coming from the reaction from the ends of the spring and the steps (and ultimately from the motor driving the escalator upwards, of course).

No, in both cases the force of gravity on the Slinky is exactly the same, and in both cases the reaction forces on the ends of the spring are the same. The escalator motor is simply ensuring that the escalator stays at a constant velocity.

I think that a stairway and an escalator provide TOTALLY different experience...for one, an escalator has continuous input of energy; whereas the stairway is just there. As mentioned before, an escalator would slap from below a bouncing ball, whereas a stairway wouldn't.

How does the ball know that?

What makes you think an escalator slaps from the bottom?

Again, in a dark warehouse, what test could you do to tell whether you are on a set of stairs or on an escalator?

Consider, once you remove the practical aspects of an escalator of finite length, what you have is a static piece of stairway moving vertically upward with inertial motion. Laws of motion tell us that there IS no difference. You might as well be on a set of stairs that's stationary while the warehouse is descending around you.

P.D. by the way, just to add that the reason I see for developing a back spin at the escalator is because the escalator step is moving at an angle but but the ball is coming down vertically...think about it, try to land on a moving surface while your center of gravity is coming down...you will feel that your feet are going away from under you...right?

No. Once you or the ball has the bit of horizontal motion imparted upon it, it has no reason to stop moving horizontally.

Think of horizontal people movers at the airport. Once it has brought you up to walking speed, you are moving inertially. You don;t feel a constant pull backwards. And if you bounced a ball while on this people mover, it would go straight up and down just as if you weren't moving at all.

Look at this from a point of view of Galilean Relativity. A staircase is at rest in the inertial frame defined by the Earth. You can also define an inertial frame in which the steps in the centre portion of the escalator are at rest. The force of gravity will be the same in both frames. For the Slinky, there is no difference.

No. Once you or the ball has the bit of horizontal motion imparted upon it, it has no reason to stop moving horizontally.

Think of horizontal people movers at the airport. Once it has brought you up to walking speed, you are moving inertially. You don;t feel a constant pull backwards. And if you bounced a ball while on this people mover, it would go straight up and down just as if you weren't moving at all.

Hold on...aren't you changing MY exercise? or forgetting my initial condition?...you said "once the ball has horizontal motion"...that's a bit afterwards or a different initial condition...I said, if I drop the ball vertically!

If I am dropped from a stationary position into a stairway or an escalator, I am sure I will be able to tell you which one it is, you know, after I wipe off the blood from my nose.

Sure, if you give me the same horizontal speed as the escalator or people mover...that's a different story (initial condition).

Hold on...aren't you changing MY exercise? or forgetting my initial condition?...you said "once the ball has horizontal motion"...that's a bit afterwards or a different initial condition...I said, if I drop the ball vertically!

I'm not changing your exercise. You were not specific.

In both the frame of the reference of the stairs and in the frame of reference of the escalator, a ball dropped vertically will come to rest on the step and have no horizontal motion. So, this test does not distinguish the difference.

I suspect that when you were speaking of "a ball being dropped vertically", what you meant (but did not specify) is with respect to the warehouse that the escalator/stairs are housed in. i.e. outside the system being examined.